Is 2sin^2(x/2)=(sin^2(x))/(1+cos(x)) ?

The answer to whether 2sin^2(x/2)=(sin^2(x))/(1+cos(x)) is True

Popular >

prove 2sin^2(x/2)=(sin^2(x))/(1+cos(x))

prove

2 sin^{2} (\frac{x}{2}) = \frac{sin ^{2} ( x )}{1 + cos ( x )}

True

Solution steps

2 sin^{2} (\frac{x}{2}) = \frac{sin ^{2} ( x )}{1 + cos ( x )}

Let:

u = \frac{x}{2}

2 sin^{2} (u) = \frac{sin ^{2} ( 2 u )}{1 + cos ( 2 u )}

Prove

2 sin^{2} (u) = \frac{sin ^{2} ( 2 u )}{1 + cos ( 2 u )} :

True

Therefore

2 sin^{2} (\frac{x}{2}) = \frac{sin ^{2} ( x )}{1 + cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

sin (b) cos^{2} (b) - sin (b) = - sin^{3} (b)

\frac{1}{2} (cot (θ) - tan (θ)) = cot (2 θ)

sin^{2} (\frac{x}{2}) = \frac{sec ( x ) - 1}{2 sec ( x )}

cos (θ) + tan (θ) sin (θ) = sec (θ)

cot^{2} (x) + 5 = csc^{2} (x) + 4

Is 2sin^2(x/2)=(sin^2(x))/(1+cos(x)) ?
The answer to whether 2sin^2(x/2)=(sin^2(x))/(1+cos(x)) is True